Codice  QDD223 
Titolo  Optimization of the positive principal eigenvalue for indefinite fractional Neumann problems 
Data  20160827 
Autore/i  Pellacci, B.; Verzinii, G. 
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Abstract  We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamic. Our main result concerns the optimization of such eigenvalue with respect to the fractional order s in (0,1], the case s = 1 corresponding to the standard Neumann Laplacian: when the habitat is not too hostile in average, the principal positive eigenvalue can not have local minima for 0 < s < 1. As a consequence, the best strategy for survival is either following the diffusion with the lowest possible s, or with s = 1, depending on the size of the domain. In addition, we show that analogous results hold for the standard fractional Laplacian in the whole space , in periodic environments. 
